All clarinetists know the high G's in Beethoven's 8th Symphony. Those notes are challenging not just because they're in the high register but because they're exposed and must be played with great control and refinement. However, the clarinet can actually play up to a fourth or even a fifth higher than those notorious G's. Check out my tutorial that gives tips as well as fingerings to get up to a double high C.
You will probably need to take in a bit more mouthpiece than usual and use a slightly harder than you may be used to. If you can get up to a double C and want to go even higher (!) you can play a double high C# and a double high D simply by overblowing the usual fingerings for those notes. Seems crazy but those notes are there. (You will have to take in LOTS of mouthpiece for those). The first time I was ever required to try and execute those notes in a piece--and "execute" might be right term here :) -- was when I was a student at Tanglewood. The year was 1980 and Gunther Schuller was the director. Towards the end of every summer there was something called the Fromm Festival--a weeklong celebration of contemporary music. I was assigned the clarinet part in Ralph Shapey's Woodwind Quintet and when I saw those double high C#'s and D's I panicked. Fortunately, however, my teacher from NEC, Peter Hadcock, was right there as a member of the Boston Symphony and gave me a quick lesson on how to meet this challenge. In his very matter-of-fact way he told me to find an incredibly hard reed, take a huge amount of mouthpiece, and basically blow the bejesus out of those notes. Which I did. And still do.